I don’t think the leading-party bashing is unique to the group. I think this is mainly because party politics become involved so people become overly passionate about it. That’s a whole other separate topic!
I also don’t think it’s as simple as your screenshot makes out:
- Councillors are busy people, often doing a day job on top of their councillor role so I doubt they get the time to easily monitor local Facebook groups.
- People are unfair to them.
- The other issue is party bias. A lib dem councillor may have bias and call on other lib dem councillors and prefer LD councillors to get the kudos over an “opponent” making the process extremely unfair.
There’s a positive for publishing all decisions and meetings every month though - it is all there, its published on the council website!
The council do do this, and they do publish bitesize announcements on their facebook and twitter accounts, and news page. I think this has improved drastically in recent years.
I do think an external body could ‘humanify’ the communications and decision making there though and say for example post it here which could be shared and engaged with so people could openly discuss it. This links back to the point made by @jtonline of improved journalism. If you know of anyone who would be interested in doing something, get them in touch 
I kicked off a news aggregator for Eastleigh a while back which has sat quietly humming not doing much: